nope

you can make it!

I know i said no you cant but there is a way you can make a flame sword. You can use this
method in anything you can hold in minecraft. First enchant your item in the anvil with
flame 1 or 2 (i forgot the numbers) and fire aspect or whatever is related with fire. Then
when you attack your opponent will burn. Dont say it doesnt work because it works for me.
Works for all version. I enchanted a bow with all the enchantment books in the anvil and
name it the 'infinity bow'. It shoots fire arrows and attacks with fire. If you cant
enchant it with fire then use all the enchantment books and it should work. If that doesnt
work then send me a private message, ill reply.